{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FZV25VAVSO3MKPIOE52HBKSXKA","short_pith_number":"pith:FZV25VAV","schema_version":"1.0","canonical_sha256":"2e6baed41593b6c53d0e277470aa57503805bb9cf06586af5c86d8407ac416f0","source":{"kind":"arxiv","id":"2504.05595","version":1},"attestation_state":"computed","paper":{"title":"A Hasse principle for $GL_2(\\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Toshiro Hiranouchi","submitted_at":"2025-04-08T01:03:32Z","abstract_excerpt":"We investigate the higher Chow groups, specifically $SK_1(E)$ for elliptic curves $E$ over number fields $F$. Focusing on the kernel $V(E)$ of the norm map $SK_1(E)\\to F^{\\times}$, we analyze its mod $p$ structure. We provide conditions, based on the mod $p$ Galois representations associated to $E$, under which the torsion subgroup of $V(E)$ is infinite."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.05595","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-04-08T01:03:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"13ad90955c180df538fcd7557a72b910df3b7294e0dfe5226ecb806def766a5f","abstract_canon_sha256":"35c75ff481c0dcc2bd2630177b9d06645cbf50c731ebab48f938dd6e739c5990"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:46:06.487490Z","signature_b64":"Xrqj1VDAg0K8UtcTxZVGn+UvU4ju72F4lyvcG2pw6LOFnUbCEo/Nyl8LucUAtqPTaYn7fleXYXWOSJIlwfi/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e6baed41593b6c53d0e277470aa57503805bb9cf06586af5c86d8407ac416f0","last_reissued_at":"2026-07-05T10:46:06.486978Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:46:06.486978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Hasse principle for $GL_2(\\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Toshiro Hiranouchi","submitted_at":"2025-04-08T01:03:32Z","abstract_excerpt":"We investigate the higher Chow groups, specifically $SK_1(E)$ for elliptic curves $E$ over number fields $F$. Focusing on the kernel $V(E)$ of the norm map $SK_1(E)\\to F^{\\times}$, we analyze its mod $p$ structure. We provide conditions, based on the mod $p$ Galois representations associated to $E$, under which the torsion subgroup of $V(E)$ is infinite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.05595","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.05595/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.05595","created_at":"2026-07-05T10:46:06.487034+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.05595v1","created_at":"2026-07-05T10:46:06.487034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.05595","created_at":"2026-07-05T10:46:06.487034+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZV25VAVSO3M","created_at":"2026-07-05T10:46:06.487034+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZV25VAVSO3MKPIO","created_at":"2026-07-05T10:46:06.487034+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZV25VAV","created_at":"2026-07-05T10:46:06.487034+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.22319","citing_title":"A Hasse principle for the higher Chow groups of curves over a global field","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA","json":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA.json","graph_json":"https://pith.science/api/pith-number/FZV25VAVSO3MKPIOE52HBKSXKA/graph.json","events_json":"https://pith.science/api/pith-number/FZV25VAVSO3MKPIOE52HBKSXKA/events.json","paper":"https://pith.science/paper/FZV25VAV"},"agent_actions":{"view_html":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA","download_json":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA.json","view_paper":"https://pith.science/paper/FZV25VAV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.05595&json=true","fetch_graph":"https://pith.science/api/pith-number/FZV25VAVSO3MKPIOE52HBKSXKA/graph.json","fetch_events":"https://pith.science/api/pith-number/FZV25VAVSO3MKPIOE52HBKSXKA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA/action/storage_attestation","attest_author":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA/action/author_attestation","sign_citation":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA/action/citation_signature","submit_replication":"https://pith.science/pith/FZV25VAVSO3MKPIOE52HBKSXKA/action/replication_record"}},"created_at":"2026-07-05T10:46:06.487034+00:00","updated_at":"2026-07-05T10:46:06.487034+00:00"}